Combining feature selection and surrogate models for the forecast of material concentration in fluids

ABSTRACT

Embodiments for intelligent forecasting of material concentrations in a fluid by a processor in a computing environment. A material concentration of a material in a fluid may be predicted according to one or more continuous stirred tank reactor (CSTR) surrogate models on statistical flow trajectories of the fluid defined by a principle component analysis (PCA) operation of a system.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates in general to forecasting materialconcentrations in fluids using a computing system, and more particularlyto, various embodiments combining feature selection and surrogate modelsfor the forecast of material concentration in fluids by a processor in acomputing environment.

Description of the Related Art

In today's interconnected and complex society, computers andcomputer-driven equipment are more commonplace. Processing devices, withthe advent and further miniaturization of integrated circuits, have madeit possible to be integrated into a wide variety of devices.Accordingly, the use of computers, network appliances, and similar dataprocessing devices continue to proliferate throughout society,particularly in the physical sciences such as, for example, fluidmechanics.

SUMMARY OF THE INVENTION

Various embodiments for intelligent forecasting of materialconcentrations in a fluid by a processor in a computing environment, areprovided. In one embodiment, by way of example only, a method forintelligent forecasting of material concentrations in a fluid, again bya processor, is provided. A material concentration of a material in afluid may be predicted according to one or more continuous stirred tankreactor (CSTR) surrogate models on statistical flow trajectories of thefluid defined by a principle component analysis (PCA) operation of asystem.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the advantages of the invention will be readilyunderstood, a more particular description of the invention brieflydescribed above will be rendered by reference to specific embodimentsthat are illustrated in the appended drawings. Understanding that thesedrawings depict only typical embodiments of the invention and are nottherefore to be considered to be limiting of its scope, the inventionwill be described and explained with additional specificity and detailthrough the use of the accompanying drawings, in which:

FIG. 1 is a block diagram depicting an exemplary computing nodeaccording to an embodiment of the present invention;

FIG. 2 is an additional block diagram depicting an exemplary cloudcomputing environment according to an embodiment of the presentinvention;

FIG. 3 is an additional block diagram depicting abstraction model layersaccording to an embodiment of the present invention;

FIG. 4 is an additional block diagram depicting various user hardwareand cloud computing components functioning in accordance with aspects ofthe present invention;

FIG. 5 is an additional block diagram depicting intelligent forecastingof material concentrations in a fluid in accordance with aspects of thepresent invention;

FIG. 6 is a flowchart diagram depicting an exemplary method forintelligent forecasting of material concentrations in fluids by aprocessor within a cloud computing environment in which various aspectsof the present invention may be realized;

FIG. 7 is a block/flow diagram depicting intelligent forecasting ofmaterial concentrations in a fluid in accordance with aspects of thepresent invention; and

FIG. 8 is a flowchart diagram depicting an exemplary method forintelligent forecasting of material concentrations in a fluid in acomputing environment, again in which various aspects of the presentinvention may be realized.

DETAILED DESCRIPTION OF THE DRAWINGS

As computing systems continue to increase in technological advancement,the demand for sophisticated prediction, forecasting, and modeling ofvarious services also grows. Many industries such as, for example, thephysical sciences, rely on critical information for forecasting andprediction. For example, fluid mechanics is the study of the mechanicsof fluids (e.g., liquids, gases, and plasmas) and the forces upon them.Fluid mechanics may include the fluid dynamics that describe the flow offluids. Convection may be the movement of a fluid and advection may bethe movement of some material dissolved or suspended in the fluid.Advection may also be the transport of a substance by bulk motion or themovement of some quantity via the bulk flow of a fluid. Duringadvection, a fluid may transport some conserved quantity or material viabulk motion. The fluid's motion may be described mathematically as afield vector and the transported material may be described by a scalarfield showing its distribution over space. Diffusion may be a netmovement of molecules or atoms from a region of high concentration to aregion of low concentration. Fluid dynamics may apply to a wide range ofapplications. Because fluids may be transported or be in motion, manyfluid flow models may be used for sophisticated prediction, forecasting,and modeling of various services.

Thus, the present invention provides for intelligent forecasting ofmaterial concentrations in a fluid by a processor in a computingenvironment. The present invention provides for surrogate modeling ofadvection-diffusion processes (e.g., transport of substances withinchemical reactors and transport of pollutants within freshwater), suchas for weather or oceanic conditions, for predicting material densitiesin fluids. Prediction of the advection-diffusion of a fluid body may beperformed using an advection-diffusion model of high resolution.Accurate long-term predictions of material densities may be obtainedfrom an advection-diffusion model output without the drawback ofrequiring long simulation periods of days to weeks (e.g., environmentalrisk assessment).

However, given that the computation of the uncertainty in materialdensities requires a large number of simulations, which render thecomputational cost of advection-diffusion models prohibitive, thepresent invention provides for using surrogate models that mimic thebehavior of advection-diffusion models while increasing computingefficiency such as, for example, by reducing computational times. In oneaspect, one or more surrogate model configurations may be developed fora selected space containing the fluid.

In an additional aspect, material concentration of a material in a fluidmay be predicted according to one or more continuous stirred tankreactor (CSTR) surrogate models on statistical flow trajectories of thefluid defined by a principle component analysis (PCA) operation of asystem. In one aspect, the mechanisms of the illustrated embodimentsprovide for the setup of surrogate models, using CSTRs on statisticalflow trajectories of the fluid defined by a principal component analysis(PCA) of a physical system, in order to predict material concentrationsin fluids. One or more CSTR surrogate models and PCA analysis may beused to predict, with low computational complexity, materialconcentrations in fluids. The CSTR surrogate models may be parameterizedvia the PCA analysis of a physical model to predict concentrations influids. The CSTR surrogate models may be dynamically configured via PCAanalysis of a physical model to predict.

In one aspect, a PCA operation may be a statistical procedure that usesan orthogonal transformation to convert a set of observations ofpossibly correlated flow trajectories into a set of values of linearlyuncorrelated variables called principal components (“PC”) (or principalmodes of variation). That is, a principal component may be a linearlyuncorrelated variable that represents a flow trajectory followingtransformation through the PCA process. The number of PCs may be lessthan or equal to the smaller of the number of original flow trajectoriesobserved in the output of the advection-diffusion physical model. Thistransformation is defined in such a way that the first PC may have alargest possible variance (that is, accounts for as much of thevariability in the data as possible), and each succeeding component inturn has the largest variance possible under the constraint that it isorthogonal to the preceding components. The resulting vectors may be anuncorrelated orthogonal basis set. PCA may also be sensitive to therelative scaling of the original variables (flow trajectories).

Other examples of various aspects of the illustrated embodiments, andcorresponding benefits, will be described further herein.

It is understood in advance that although this disclosure includes adetailed description on a computing system, the computing system may bea cloud computing system, and the implementation of the teachingsrecited herein are not limited to a cloud computing environment orInternet of Things (IoT) network environment. Rather, embodiments of thepresent invention are capable of being implemented in conjunction withany other type of computing environment now known or later developed. Itshould be noted that the IoT is an emerging concept involving computingdevices that may be embedded in objects, such as appliances, andconnected through a network. An IoT network may include one or more IoTdevices or “smart devices”, which are physical objects such asappliances with computing devices embedded therein. Many IoT devices areindependently operable, but they also may be paired with a controlsystem or with a distributed control system such as one running over acloud computing environment. The control system may include anend-to-end flow monitoring mechanism similar to the one describedherein.

Cloud computing is a model of service delivery for enabling convenient,on-demand network access to a shared pool of configurable computingresources (e.g. networks, network bandwidth, servers, processing,memory, storage, applications, virtual machines, and services) that canbe rapidly provisioned and released with minimal management effort orinteraction with a provider of the service. This cloud model may includeat least five characteristics, at least three service models, and atleast four deployment models.

Characteristics are as follows:

On-demand self-service: a cloud consumer can unilaterally provisioncomputing capabilities, such as server time and network storage, asneeded automatically without requiring human interaction with theservice's provider.

Broad network access: capabilities are available over a network andaccessed through standard mechanisms that promote use by heterogeneousthin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

Resource pooling: the provider's computing resources are pooled to servemultiple consumers using a multi-tenant model, with different physicaland virtual resources dynamically assigned and reassigned according todemand. There is a sense of location independence in that the consumergenerally has no control or knowledge over the exact location of theprovided resources but may be able to specify location at a higher levelof abstraction (e.g., country, state, or datacenter).

Rapid elasticity: capabilities can be rapidly and elasticallyprovisioned, in some cases automatically, to quickly scale out andrapidly released to quickly scale in. To the consumer, the capabilitiesavailable for provisioning often appear to be unlimited and can bepurchased in any quantity at any time.

Measured service: cloud systems automatically control and optimizeresource use by leveraging a metering capability at some level ofabstraction appropriate to the type of service (e.g., storage,processing, bandwidth, and active user accounts). Resource usage can bemonitored, controlled, and reported providing transparency for both theprovider and consumer of the utilized service.

Service Models are as follows:

Software as a Service (SaaS): the capability provided to the consumer isto use the provider's applications running on a cloud infrastructure.The applications are accessible from various client devices through athin client interface such as a web browser (e.g., web-based e-mail).The consumer does not manage or control the underlying cloudinfrastructure including network, servers, operating systems, storage,or even individual application capabilities, with the possible exceptionof limited user-specific application configuration settings.

Platform as a Service (PaaS): the capability provided to the consumer isto deploy onto the cloud infrastructure consumer-created or acquiredapplications created using programming languages and tools supported bythe provider. The consumer does not manage or control the underlyingcloud infrastructure including networks, servers, operating systems, orstorage, but has control over the deployed applications and possiblyapplication hosting environment configurations.

Infrastructure as a Service (IaaS): the capability provided to theconsumer is to provision processing, storage, networks, and otherfundamental computing resources where the consumer is able to deploy andrun arbitrary software, which can include operating systems andapplications. The consumer does not manage or control the underlyingcloud infrastructure but has control over operating systems, storage,deployed applications, and possibly limited control of select networkingcomponents (e.g., host firewalls).

Deployment Models are as follows:

Private cloud: the cloud infrastructure is operated solely for anorganization. It may be managed by the organization or a third party andmay exist on-premises or off-premises.

Community cloud: the cloud infrastructure is shared by severalorganizations and supports a specific community that has shared concerns(e.g., mission, security requirements, policy, and complianceconsiderations). It may be managed by the organizations or a third partyand may exist on-premises or off-premises.

Public cloud: the cloud infrastructure is made available to the generalpublic or a large industry group and is owned by an organization sellingcloud services.

Hybrid cloud: the cloud infrastructure is a composition of two or moreclouds (private, community, or public) that remain unique entities butare bound together by standardized or proprietary technology thatenables data and application portability (e.g., cloud bursting forload-balancing between clouds).

A cloud computing environment is service oriented with a focus onstatelessness, low coupling, modularity, and semantic interoperability.At the heart of cloud computing is an infrastructure comprising anetwork of interconnected nodes.

Referring now to FIG. 1, a schematic of an example of a cloud computingnode is shown. Cloud computing node 10 is only one example of a suitablecloud computing node and is not intended to suggest any limitation as tothe scope of use or functionality of embodiments of the inventiondescribed herein. Regardless, cloud computing node 10 is capable ofbeing implemented and/or performing any of the functionality set forthhereinabove.

In cloud computing node 10 there is a computer system/server 12, whichis operable with numerous other general purpose or special purposecomputing system environments or configurations. Examples of well-knowncomputing systems, environments, and/or configurations that may besuitable for use with computer system/server 12 include, but are notlimited to, personal computer systems, server computer systems, thinclients, thick clients, hand-held or laptop devices, multiprocessorsystems, microprocessor-based systems, set top boxes, programmableconsumer electronics, network PCs, minicomputer systems, mainframecomputer systems, and distributed cloud computing environments thatinclude any of the above systems or devices, and the like.

Computer system/server 12 may be described in the general context ofcomputer system-executable instructions, such as program modules, beingexecuted by a computer system. Generally, program modules may includeroutines, programs, objects, components, logic, data structures, and soon that perform particular tasks or implement particular abstract datatypes. Computer system/server 12 may be practiced in distributed cloudcomputing environments where tasks are performed by remote processingdevices that are linked through a communications network or IoT network.In a distributed cloud computing environment, program modules may belocated in both local and remote computer system storage media includingmemory storage devices.

As shown in FIG. 1, computer system/server 12 in cloud computing node 10is shown in the form of a general-purpose computing device. Thecomponents of computer system/server 12 may include, but are not limitedto, one or more processors or processing units 16, a system memory 28,and a bus 18 that couples various system components including systemmemory 28 to processor 16.

Bus 18 represents one or more of any of several types of bus structures,including a memory bus or memory controller, a peripheral bus, anaccelerated graphics port, and a processor or local bus using any of avariety of bus architectures. By way of example, and not limitation,such architectures include Industry Standard Architecture (ISA) bus,Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, VideoElectronics Standards Association (VESA) local bus, and PeripheralComponent Interconnects (PCI) bus.

Computer system/server 12 typically includes a variety of computersystem readable media. Such media may be any available media that isaccessible by computer system/server 12, and it includes both volatileand non-volatile media, removable and non-removable media.

System memory 28 can include computer system readable media in the formof volatile memory, such as random access memory (RAM) 30 and/or cachememory 32. Computer system/server 12 may further include otherremovable/non-removable, volatile/non-volatile computer system storagemedia. By way of example only, storage system 34 can be provided forreading from and writing to a non-removable, non-volatile magnetic media(not shown and typically called a “hard drive”). Although not shown, amagnetic disk drive for reading from and writing to a removable,non-volatile magnetic disk (e.g., a “floppy disk”), and an optical diskdrive for reading from or writing to a removable, non-volatile opticaldisk such as a CD-ROM, DVD-ROM or other optical media can be provided.In such instances, each can be connected to bus 18 by one or more datamedia interfaces. As will be further depicted and described below,system memory 28 may include at least one program product having a set(e.g., at least one) of program modules that are configured to carry outthe functions of embodiments of the invention.

Program/utility 40, having a set (at least one) of program modules 42,may be stored in system memory 28 by way of example, and not limitation,as well as an operating system, one or more application programs, otherprogram modules, and program data. Each of the operating system, one ormore application programs, other program modules, and program data orsome combination thereof, may include an implementation of a networkingenvironment. Program modules 42 generally carry out the functions and/ormethodologies of embodiments of the invention as described herein.

Computer system/server 12 may also communicate with one or more externaldevices 14 such as a keyboard, a pointing device, a display 24, etc.;one or more devices that enable a user to interact with computersystem/server 12; and/or any devices (e.g., network card, modem, etc.)that enable computer system/server 12 to communicate with one or moreother computing devices. Such communication can occur via Input/Output(I/O) interfaces 22. Still yet, computer system/server 12 cancommunicate with one or more networks such as a local area network(LAN), a general wide area network (WAN), an IoT network, and/or apublic network (e.g., the Internet) via network adapter 20. As depicted,network adapter 20 communicates with the other components of computersystem/server 12 via bus 18. It should be understood that although notshown, other hardware and/or software components could be used inconjunction with computer system/server 12. Examples, include, but arenot limited to: microcode, device drivers, redundant processing units,external disk drive arrays, RAID systems, tape drives, and data archivalstorage systems, etc.

Referring now to FIG. 2, illustrative cloud computing environment 50 isdepicted. As shown, cloud computing environment 50 comprises one or morecloud computing nodes 10 with which local computing devices used bycloud consumers, such as, for example, personal digital assistant (PDA)or cellular telephone 54A, desktop computer 54B, laptop computer 54C,and/or automobile computer system 54N may communicate. Nodes 10 maycommunicate with one another. They may be grouped (not shown) physicallyor virtually, in one or more networks, such as Private, Community,Public, or Hybrid Clouds as described hereinabove, or a combinationthereof. This allows cloud computing environment 50 to offerinfrastructure, platforms and/or software as services for which a cloudconsumer does not need to maintain resources on a local computingdevice. It is understood that the types of computing devices 54A-N shownin FIG. 2 are intended to be illustrative only and that computing nodes10 and cloud computing environment 50 can communicate with any type ofcomputerized device over any type of network and/or network addressableconnection (e.g., using a web browser).

Referring now to FIG. 3, a set of functional abstraction layers providedby cloud computing environment 50 (FIG. 2) is shown. It should beunderstood in advance that the components, layers, and functions shownin FIG. 3 are intended to be illustrative only and embodiments of theinvention are not limited thereto. As depicted, the following layers andcorresponding functions are provided:

Device layer 55 includes physical and/or virtual devices, embedded withand/or standalone electronics, sensors, actuators, and other objects toperform various tasks in a cloud computing environment 50. Each of thedevices in the device layer 55 incorporates networking capability toother functional abstraction layers such that information obtained fromthe devices may be provided thereto, and/or information from the otherabstraction layers may be provided to the devices. In one embodiment,the various devices inclusive of the device layer 55 may incorporate anetwork of entities collectively known as the “internet of things”(IoT). Such a network of entities allows for intercommunication,collection, and dissemination of data to accomplish a great variety ofpurposes, as one of ordinary skill in the art will appreciate.

Device layer 55 as shown includes sensor 52, actuator 53, “learning”thermostat 56 with integrated processing, sensor, and networkingelectronics, camera 57, controllable household outlet/receptacle 58, andcontrollable electrical switch 59 as shown. Other possible devices mayinclude, but are not limited to various additional sensor devices,networking devices, electronics devices (such as a remote controldevice), additional actuator devices, so called “smart” appliances suchas a refrigerator or washer/dryer, and a wide variety of other possibleinterconnected objects.

Hardware and software layer 60 includes hardware and softwarecomponents. Examples of hardware components include: mainframes 61; RISC(Reduced Instruction Set Computer) architecture based servers 62;servers 63; blade servers 64; storage devices 65; and networks andnetworking components 66. In some embodiments, software componentsinclude network application server software 67 and database software 68.

Virtualization layer 70 provides an abstraction layer from which thefollowing examples of virtual entities may be provided: virtual servers71; virtual storage 72; virtual networks 73, including virtual privatenetworks; virtual applications and operating systems 74; and virtualclients 75.

In one example, management layer 80 may provide the functions describedbelow. Resource provisioning 81 provides dynamic procurement ofcomputing resources and other resources that are utilized to performtasks within the cloud computing environment. Metering and Pricing 82provides cost tracking as resources are utilized within the cloudcomputing environment, and billing or invoicing for consumption of theseresources. In one example, these resources may comprise applicationsoftware licenses. Security provides identity verification for cloudconsumers and tasks, as well as protection for data and other resources.User portal 83 provides access to the cloud computing environment forconsumers and system administrators. Service level management 84provides cloud computing resource allocation and management such thatrequired service levels are met. Service Level Agreement (SLA) planningand fulfillment 85 provides pre-arrangement for, and procurement of,cloud computing resources for which a future requirement is anticipatedin accordance with an SLA.

Workloads layer 90 provides examples of functionality for which thecloud computing environment may be utilized. Examples of workloads andfunctions which may be provided from this layer include: mapping andnavigation 91; software development and lifecycle management 92; virtualclassroom education delivery 93; data analytics processing 94;transaction processing 95; and, in the context of the illustratedembodiments of the present invention, various configuring settings forvarious computer-controlled devices for intelligent forecasting ofmaterial concentrations in fluids (e.g., combining feature selection andsurrogate models for the forecast of material concentrations in fluids)workloads and functions 96. In addition, configuring settings forvarious computer-controlled devices using workloads and functions 96 forintelligent forecasting of material concentrations in fluids may includesuch operations as data analysis (including data collection andprocessing from various environmental sensors), semantic analysis, imageanalysis, control input analysis, device analysis, and/or data analyticsfunctions. One of ordinary skill in the art will appreciate that theconfiguring settings for various computer-controlled devices usingworkloads and functions 96 for intelligent forecasting of materialconcentrations in fluids may also work in conjunction with otherportions of the various abstractions layers, such as those in hardwareand software 60, virtualization 70, management 80, and other workloads90 (such as data analytics processing 94, for example) to accomplish thevarious purposes of the illustrated embodiments of the presentinvention.

Turning to FIG. 4, a block diagram of various hardware 400 equipped withvarious functionality as will be further described is shown in whichaspects of the mechanisms of the illustrated embodiments may berealized. In one aspect, one or more of the components, modules,services, applications, and/or functions described in FIGS. 1-3 may beused in FIG. 4. For example, computer system/server 12 of FIG. 1 may beincluded in FIG. 4 and may be connected to other computing nodes over adistributed computing network, where additional data collection,processing, analytics, and other functionality may be realized. Thecomponents of computer system/server 12 may include, but are not limitedto, one or more processors or processing units 16, a system memory 28,and a bus 18 of FIG. 1 (not shown in FIG. 4 for illustrative purposesonly) that couples various system components including system memory 28to processor 16.

The computer system/server 12 of FIG. 1 may include a materialconcentration prediction service 402 for intelligent forecasting ofmaterial concentrations in fluid within a computing environment such as,for example, a cloud computing environment, along with other relatedcomponents.

The material concentration prediction service 402 may include a materialconcentration prediction component 404 and, again, processing units 16and a system memory 28. In operation, the material concentrationprediction component 404 may establish a 3-way communication patternbetween one or more data sources (e.g., an application, database,webpage, etc.) and one or more continuous stirred tank reactors (CSTR)to enable communication flow between the data sources and one or moreCSTRs. The material concentration prediction component 404 may include adata ingestion component 406, a principle component analysis (PCA)operation component 408 (e.g., proper orthogonal decomposition), asurrogate modeling component 410, and a calibration component 412. Inone aspect, the data ingestion component 406 may be a physical-dataingestion component that may process data inputs (physical data inputs)from an advection-diffusion (AD) model (e.g., a high-resolution ADmodel) of a fluid. It should be noted that a physical input may be datainputs in the form of flow velocities and material (solute or substancein the fluid) concentrations. These physical inputs may result fromsimulations performed by the AD model. High resolution may refer to thespatial resolution of the three-dimensional mesh that represents thereal fluid body. A high resolution mesh consists of cells that arerelatively small depending on the fluid represented. For the embodimentexample, a high resolution mesh may consist of 50×50 meter cells in thehorizontal and 40 layers of variable height in the vertical (averageheight of less than 1 meter). The mesh could be much finer in thehorizontal for applications in reactor modeling.

The PCA operation component 408 may be a reduced space modelingcomponent that may perform a PCA operation on the physical inputs. ThePCA operation component 408 may parameterize one or more surrogatemodels (SM) (e.g., CSTR surrogate models) using the various physicalinputs. That is, the PCA operation component 408 may parameterize one ormore CSTR surrogate models via the PCA analysis operation of a physicalmodel to predict the material concentration of a material in a fluid.

The surrogate modeling component 410 may determine and/or computematerial densities in a fluid over a selected period of time accordingto various and different alternative arrays of CSTR systems that may beconnected in series and/or associated with each principal component. Thesurrogate modeling component 410 may dynamically configure one or moreCSTR surrogate models via a PCA analysis operation of a physical modelto predict the material concentration of a material in a fluid.

The calibration component 412 may adjust one or more parameters of thePCA operation component 408 based on an output of the AD model.

Thus, the material concentration prediction service 402 may providesignificant reductions in time required to predict material densitieswith respect to one or more AD model simulations. The materialconcentration prediction service 402 increases the accuracy of thepredicting and forecasting material concentrations in a fluid. Thematerial concentration prediction service 402 is flexible by enabling auser or administrator to adjust or manipulate a size of feature space(e.g., a space containing a fluid) to accurately resolve complex flowsof the fluid in the reduced space.

Turning now to FIG. 5, a block diagram of exemplary functionality 500relating to intelligent forecasting of material concentrations in afluid is depicted. As will be seen, many of the functional blocks mayalso be considered “modules” of functionality, in the same descriptivesense as has been previously described in FIGS. 1-4. With the foregoingin mind, the module blocks 500 may also be incorporated into varioushardware and software components of a system for intelligent forecastingof material concentrations in a fluid in a cloud-computing environmentin accordance with the present invention, such as those described inFIGS. 1-4. Many of the functional blocks 500 may execute as backgroundprocesses on various components, either in distributed computingcomponents, or on the user device, or elsewhere.

Starting with block 502, a physical model 502, such as anadvection-diffusion (AD) model, is shown. In the Physical Space Module(1), a real fluid system may be represented by means of ahigh-resolution advection-diffusion model (physical model) 502. Thisphysical model may simulate the hydrodynamics within the fluid andcalculate flow trajectories and material concentrations within thefluid. The physical model output (not the model itself) may be theelement of concern or interest. Historical advection-diffusion (AD) datasource (physical module) may be used and defined. As shown in block 508,historical AD data (e.g., historical flow data) may be retrieved. The ADhistorical data may be processed statistically (e.g., compute depthaverages). Using a fluid velocity grid, one or more AD fluid flowtrajectories may be identified. Also, one or more physical properties ofthe system (geometric model, grid discretization, boundary and initialconditions) may be analyzed.

As indicated in block 504, one or more feature selection parameters maybe input for a PCA operation. The input parameters (e.g., user providedinput parameters) may be processed and analyzed so as to determineand/or identify 1) a maximum number of principal components (PCs) (e.g.,N number of PCs such as, for example, PC₁, PC₂, and PC_(n), where N is apositive integer or selected number), 2) a maximum number of CSTRs perPC, and 3) convergence criteria. A transformations operation may beperformed to convert flow trajectories into PCs. Also, one or moresurrogate model parameters may be defined.

The historical flow data 508 produced by the physical model may be usedas input to a reduced space module (2), where a feature selectionoperation may identify the fluid's dominant advection-diffusioncharacteristics using principal component analysis (PCA), as indicatedin blocks 504, 510, and 512. The feature selection operation maycalculate the portion of the flow variability explained by eachprincipal component (e.g., PC₁, PC₂, and PC_(N)) and assigns thesevariances as a coefficient CV_(i) to each component, where CV_(i) is thevariance and C₀ is the initial concentration of material. The moduledistributes the initial concentration of the material (C₀) of interestand the total flow through the fluid system based on nonlinear functionsf₁ and f₂ of the coefficients of variance CV_(i). A variance explained(CV) may be provided for each PC such as, for example, PCi for CVi,where “i” is a variable or positive integer.

In the Surrogate Model Module (3), one or more surrogate models, asillustrated in block 506, may be built consisting of a series of CSTRs,as shown collectively in block 514, assigned to each PCA trajectory,identified in 510, where the number of CSTRs m_(i) may be variable. Inassociation with block 506, block 514 may include one or more CSTRarrays (which may be connected in series) associated with one or morePCs. For example, PC₁ may be associated with CSTR 1.1, 1.2, and 1.m₁.PC₂ may be associated with CSTR 2.1, 2.2, and 2.m₂. PC_(N) may beassociated with CSTR N.1, N.2, and N.m_(N). Also, one or more surrogatemodels may determine or predict the material densities over a selectedtime period such as, for example, over residence time (RT) time periodsfor each one of the various and alternative configurations of the CSTRsconnected, which may be connected in series and associated with eachprinciple component (PC).

A coupled system of differential equations, as illustrated in block 506,may be assigned to each CSTR series and solved to determine theconcentration and residence time of material through each PCAtrajectory, such as, for example, the coupled system of differentialequations of:

C ₁ ′+f ₁(t)C ₁=0,

C ₂ ′+f ₂(t)(C ₂ −C ₁)=0, . . . and

C _(n) ′+f _(n)(t)(C _(n) −C _(n-1))=0

where C is the initial concentration of the material in the fluid and tis time. The parameters of the f₁ and f₂ functions, as well as thenumber of CSTRs, and additional parameters to describe the CSTR-basedsurrogate model are calibrated iteratively using an optimizationalgorithm.

As depicted in block 512, one or more CSTR surrogate models may beparameterized using the PCA operation of a physical model of the systemfor the predicting. That is, block 512 illustrates a parameterization ofthe surrogate model and estimates initial material concentrations andtotal flows for each principal component. These flows are necessary asinput to the CSTR based surrogate model of block 514. In one aspect, theparameterization of the surrogate model and estimates may be performedusing equations:

C _(0PCi) =f ₁(CV_(i))C ₀,  (1), and

Q _(PCi) =f ₂(CV_(i))Q _(T),  (2)

where C_(0PCi) is the initial material concentration assigned toprincipal component i (i=1, . . . , N), f₁(CV_(i)) is a nonlinearfunction of the coefficient of variance explained CV_(i), C₀ is theinitial average concentration of the material in the whole fluid body,Q_(PCi) is the inflow rate of fluid allocated to principal component i,f₂ (CV_(i)) is another nonlinear function of CV_(i), and Q_(T) is thetotal inflow rate of fluid provided to the fluid system.Parameterization focuses on calibrating the parameters of the nonlinearfunctions f₁ and f₂ starting from arbitrary initial values that aretuned iteratively using the processes of blocks 506, 512, and 514.

Turning now to FIG. 6, a method 600 for intelligent forecasting ofmaterial concentrations in fluids by a processor within a cloudcomputing environment is depicted. In one aspect, each of the devices,components, modules, operations, and/or functions described in FIGS. 1-5also may apply or perform one or more operations or actions of FIG. 6.The functionality 600 may be implemented as a method executed asinstructions on a machine, where the instructions are included on atleast one computer readable medium or one non-transitory machinereadable storage medium. The functionality 600 may start in block 602,for a physical space (e.g., generation of historical AD data forcalibration). One or more simulation parameters may be collected,processed, and/or analyzed, as in block 604. One or more various fluidmodels may be performed on the simulation parameters, as in block 606. Adetermination operation may be performed to determine the success of thesimulation, as in block 608. If yes at block 608, the functionality 600may move to block 612 and provide the historical AD fluid flow data, andthen end at block 614. If no at block 608, the input parameters may bemodified, as in block 610, where the functionality may then return toblock 606.

Starting in block 616, the historical AD fluid flow data (from block612) may be retrieved and used for feature selection parameters, as inblock 618. A PCA operation may be performed, as in block 620. Adetermination operation may be performed to determine the success of thePCA operation, as in block 622. If no at block 622, the input parametersmay be modified, as in block 624, where the functionality may thenreturn to block 618. If yes at block 622, the functionality 600 may moveto block 626 and identify N number of principal components (PC). Fromblock 626, the functionality may move to block 628 where one or moresurrogate models may be parametrized using the PCA operation (e.g.,variance explanation) of a physical model of the system for thepredicting. One or more arrays of N CSTR systems may be organized and/orbuilt, as in block 630. A system of ODEs may be assembled, as in block632. The system of ODEs may be determined and/or calculated, as in block634. The material concentration of a material in a fluid may bepredicted, as in block 636. One or more the surrogate models may beevaluated to identify erroneous surrogate models so as to dynamicallyconfigure the one or more surrogate models according to the PCAoperation of the system for the predicting, as in block 638. Adetermination operation may be performed, at block 640, to determine ifthe identified erroneous surrogate models required no configurations. Ifno at block 640, the functionality may move to block 628. If yes atblock 640, the one or more surrogate models may predict the materialdensities, as in block 642. The functionality 600 may end at block 644.

FIG. 7 is a chart diagram 700 for intelligent forecasting of materialconcentrations in fluids. More specifically, FIG. 7 summarizes apreliminary use case assessment and comparison on the predictiveaccuracy of the proposed invention in predicting the long-term decay ofsalt, represented as a conservative tracer. The goal of this assessmentis to illustrate the benefits of the present invention (PCA andsurrogate model) compared to a surrogate model (SM) based on a singleseries of CSTRs (as opposed to the dynamically adjusted series of CSTRsfor each principal component of the present invention).

Diagram 720 of FIG. 7 presents a graphical representation of thehigh-resolution AD model of the fluid body (in this case a body of watersuch as a lake). Said differently, the chart diagram includes the highresolution physical model of the body of water 720 (e.g., a lake havinga north basin region, a narrows region, and a south basin region). Thephysical parameters and data inputs may be transferred to a surrogatemodel. Three benchmark simulations were performed using the AD model:(1) under DRY conditions, the detailed total inflows to the lake in theform of runoff and direct precipitation were decreased by 20% withrespect to normally observed values; (2) under NORMAL conditions, theobserved detailed inflows were applied; and (3) under WET conditions,the observed normal inflows were increased by 20% with respect to theobserved inflows. Each simulation took approximately 9.7 E6 seconds torun as indicated in the table/graph 750. The results of the simulationsin the form of flow trajectories and tracer concentrations were storedto be used as input for the PCA and surrogate model (e.g., PCA-SM) basedaspects of the present invention.

The chart diagram 700 depicts graph 725 presenting a graphical summaryof the prediction accuracy assessment of a simple surrogate model (SM)and our invention (PCA) with respect to the benchmark simulationresults. Chart 725 depicts showing the performance of the surrogatemodels and PCA operations for three inflow fluid scenarios such as, forexample, dry, normal, and/or wet as defined or selected based onconditions for a selected region, with the root mean squared error(RMSE) on the y-axis and the number (No.) of CSTRs and methods on theX-axis of graph 725. The graph 725 depicts a performance comparison ofthe surrogate models (SM) and the PCA model (e.g., PCA-SM) for normaland extreme wet/dry conditions (+/−20%) lake inflow scenarios. ThePCA-SM model methods use 3 PCAs which account for 89% of the flowvariance.

Said differently, graph 725 illustrates for each simulation scenario(dry, normal, and wet), in the vertical axis, the root mean squarederror (RMSE) of the SM and PCA operations with respect to the benchmarksand, in the horizontal axis, the number of CSTRs assigned to SM and PCA.To clarify, 1 to 3 CSTRs were assigned to each SM and PCA model, whichmeans that the SM model consists of a single series of 1 to 3 CSTRs. Thepresent invention PCA (e.g., PCA-SM model) assigns 1 to 3 CSTRs to eachprincipal component. The PCA method (e.g., PCA-SM model) of the presentinvention outperforms (smaller RMSE) the SM method except for the dryscenario. This means (1) these results relied on a preliminaryimplementation of the dynamic calibration process, so further tuning maylead to outperforming the SM also for the dry scenario; and (2) the dryand wet scenarios are somewhat unrealistic since they are extremeconsidering the historical trends on precipitation; thus more weight maybe placed on the results obtained for the normal scenario.

The chart diagram 700 also depicts graph 750 illustrating a comparisonof dye decay predictions. Graph 750 illustrates long term tracer decaypredictions by the AD model (e.g., environmental fluid dynamics code“EFDC”), the PCA (e.g., PCA-SM) of the embodiments described herein, andthe surrogate model (SM) for the normal inflow simulation scenario.Better agreement is observed between PCA and EFDC. The simulation timeby PCA (e.g., PCA-SM) is slightly larger than that of SM, but stillsmall enough to reduce the AD model times by 7 orders of magnitude.

The computation times of the EFDC shows 9.7 E6 seconds, the surrogatemodel as 0.1, and the PCA as 0.9 over a selected period of time, wheretime (e.g., years) is depicted on the X-axis and the percentage ofconcentration of the material in a fluid is depicted on the Y-axis.Chart 750 shows a 60-year simulation period between the PCA predictionsand a baseline AD (e.g., environmental fluid dynamics code “EFDC”) data.The computational time for the EFDC is shown as 16 weeks and therequired time for the SM is one or more orders of smaller magnitude.

Turning now to FIG. 8, a method 800 for intelligent forecasting ofmaterial concentrations in fluids by a processor within a cloudcomputing environment is depicted. In one aspect, each of the devices,components, modules, operations, and/or functions described in FIGS. 1-7also may apply or perform one or more operations or actions of FIG. 8.The functionality 800 may be implemented as a method executed asinstructions on a machine, where the instructions are included on atleast one computer readable medium or one non-transitory machinereadable storage medium. The functionality 800 may start in block 802. Amaterial concentration of a material in a fluid may be predictedaccording to one or more continuous stirred tank reactor (CSTR)surrogate models on statistical flow trajectories of the fluid definedby a principle component analysis (PCA) operation of a system, as inblock 804. The functionality 800 may end, as in block 806.

In one aspect, in conjunction with and/or as part of at least one blockof FIG. 8, the operations of method 800 may include each of thefollowing. The operations of method 800 may predict low computationalcomplexity material concentrations in the fluid using the one or moreCSTR surrogate models and the PCA operation. One or more CSTR surrogatemodels may be parameterized using the PCA operation of a physical modelof the system for the predicting.

The operations of method 800 may dynamically configure the one or moreCSTR surrogate models according to the PCA operation of the system forthe predicting, wherein the system is one or more CSTR systems connectedin series. One or more features and parameters may be selected fromhistorical flow data of the material. The operations of method 800 mayanalyze and process input data from an advection-diffusion (AD) model ofthe fluid.

The PCA operation may also include at least analyzing one or more inputparameters so as to determine a maximum number of material components, amaximum number of CSTR systems per each one of the material components,and criteria for convergence; converting material flow trajectories intoeach one of the material components; and/or defining one or moreparameters for the CSTR surrogate models.

The operations of method 800 may calibrate the one or more CSTRsurrogate models by adjusting one or more parameters of the PCAoperation.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowcharts and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowcharts and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowcharts and/or block diagram block orblocks.

The flowcharts and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowcharts or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustrations, and combinations ofblocks in the block diagrams and/or flowchart illustrations, can beimplemented by special purpose hardware-based systems that perform thespecified functions or acts or carry out combinations of special purposehardware and computer instructions.

1. A method for intelligent forecasting of material concentrations in afluid by a processor within a cloud computing environment, comprising:predicting a material concentration of a material in a fluid accordingto one or more continuous stirred tank reactor (CSTR) surrogate modelson statistical flow trajectories of the fluid defined by a principlecomponent analysis (PCA) operation of a system.
 2. The method of claim1, further including defining the one or more CSTR surrogate modelsaccording to the PCA operation.
 3. The method of claim 1, furtherincluding parameterizing the one or more CSTR surrogate models using thePCA operation of a physical model of the system for the predicting. 4.The method of claim 1, further including dynamically configuring the oneor more CSTR surrogate models according to the PCA operation of thesystem for the predicting, wherein the system is one or more CSTRsystems connected in series.
 5. The method of claim 1, further includingselecting one or more features and parameters from historical flow dataof the material.
 6. The method of claim 1, further including analyzingand processing input data from an advection-diffusion (AD) model of thefluid.
 7. The method of claim 1, wherein the PCA operation includes atleast: analyzing one or more input parameters so as to determine amaximum number of principal components (PCs), a maximum number of CSTRsystems per each one of the PCs, and criteria for convergence;converting material flow trajectories into each one of the PCs; anddefining one or more parameters for the CSTR surrogate models.
 8. Themethod of claim 1, further including calibrating the one or more CSTRsurrogate models by adjusting one or more parameters of the PCAoperation.
 9. A system for intelligent forecasting of materialconcentrations in a fluid within a computing environment, comprising:one or more computers with executable instructions that when executedcause the system to: predict a material concentration of a material in afluid according to one or more continuous stirred tank reactor (CSTR)surrogate models on statistical flow trajectories of the fluid definedby a principle component analysis (PCA) operation of a system.
 10. Thesystem of claim 9, wherein the executable instructions further definethe one or more CSTR surrogate models according to the PCA operation.11. The system of claim 9, wherein the executable instructions furtherparameterize the one or more CSTR surrogate models using the PCAoperation of a physical model of the system for the predicting.
 12. Thesystem of claim 9, wherein the executable instructions furtherdynamically configure the one or more CSTR surrogate models according tothe PCA operation of the system for the predicting, wherein the systemis one or more CSTR systems connected in series.
 13. The system of claim9, wherein the executable instructions further select one or morefeatures and parameters from historical flow data of the material. 14.The system of claim 9, wherein the executable instructions furtheranalyze and process input data from an advection-diffusion (AD) model ofthe fluid.
 15. The system of claim 9, wherein the executableinstructions further: analyze one or more input parameters so as todetermine a maximum number of principal components (PCs), a maximumnumber of CSTR systems per each one of the PCs, and criteria forconvergence; convert material flow trajectories into each one of thePCs; define one or more parameters for the CSTR surrogate models; andcalibrate the one or more CSTR surrogate models by adjusting one or moreparameters of the PCA operation.
 16. A computer program product for, bya processor, intelligent forecasting of material concentrations in afluid, the computer program product comprising a non-transitorycomputer-readable storage medium having computer-readable program codeportions stored therein, the computer-readable program code portionscomprising: an executable portion that predicts a material concentrationof a material in a fluid according to one or more continuous stirredtank reactor (CSTR) surrogate models on statistical flow trajectories ofthe fluid defined by a principle component analysis (PCA) operation of asystem.
 17. The computer program product of claim 16, further includingan executable portion that defines the one or more CSTR surrogate modelsaccording to the PCA operation.
 18. The computer program product ofclaim 16, further including an executable portion that parameterizes theone or more CSTR surrogate models using the PCA operation of a physicalmodel of the system for the predicting.
 19. The computer program productof claim 16, further including an executable portion that dynamicallyconfigures the one or more CSTR surrogate models according to the PCAoperation of the system for the predicting, wherein the system is one ormore CSTR systems connected in series.
 20. The computer program productof claim 16, further including an executable portion that selects one ormore features and parameters from historical flow data of the material.21. The computer program product of claim 16, further including anexecutable portion that analyzes and processes input data from anadvection-diffusion (AD) model of the fluid.
 22. The computer programproduct of claim 16, wherein the PCA operation further includes atleast: analyzing one or more input parameters so as to determine amaximum number of principal components (PCs), a maximum number of CSTRsystems per each one of the PCs, and criteria for convergence;converting material flow trajectories into each one of the PCs; anddefining one or more parameters for the CSTR surrogate models.
 23. Thecomputer program product of claim 16, further including an executableportion that calibrates the one or more CSTR surrogate models byadjusting one or more parameters of the PCA operation.